A180135 Smallest k such that k*11^n is a sum of two successive primes.

5, 18, 6, 24, 6, 32, 40, 26, 20, 94, 50, 26, 10, 168, 30, 18, 196, 126, 70, 166, 30, 54, 130, 26, 50, 10, 40, 28, 20, 120, 84, 26, 228, 336, 92, 174, 24, 308, 28, 102, 216, 232, 68, 112, 192, 252, 512, 302, 110, 10, 330, 30, 138, 150, 168, 770, 70, 264, 24, 72, 180, 198

Offset

0,1

Comments

If a(n) == 0 (mod 11), then a(n+1) = a(n)/11.

Records: 5, 18, 24, 32, 40, 94, 168, 196, 228, 336, 512, 770, 996, 1446, 1644, 1812, 1900, 3840, ..., .

Corresponding primes are twin primes for n = 0, 3, ..., .

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..200

Mathematica

f[n_] := Block[{k = 1, j = 11^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]

Prog

(Python)
from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow11 = 1, 11**n
  while not ok(k*pow11): k += 1
  return k
print([a(n) for n in range(62)]) # Michael S. Branicky, May 18 2021

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180136, A180137, A180138.

Sequence in context: A097491 A120087 A353690 * A260080 A178365 A345912

Adjacent sequences: A180132 A180133 A180134 * A180136 A180137 A180138

Keyword

base,nonn

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Status

approved